Finite Group Databasebeta

← #94115

Subgroups — #94115

Order 512.

262 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1327C212yesmaximal
2#10845C211yesmaximal, characteristic
3C2×#423C411yescharacteristic
4C2×#423C2211yescharacteristic
5C22×#97C411yescharacteristic
6C2×#349—22no—
7C2×#341—22no—
8#1327—22no—
9#1327C414yes—
10C22×M16—21no—
11C22×M16D412yes—
12C23×C8—21no—
13C22×C42C2×C411yescharacteristic
14C2×M32—42no—
15#423—21no—
16#423—41no—
17#423—41no—
18#423C812yes—
19#423C2×C412yes—
20#423D411yescharacteristic
21#423Q811yescharacteristic
22C2×C4⋊C8—41no—
23C2×C4⋊C8—41no—
24C2×#97—21no—
25C2×#97—41no—
26C2×#97—41no—
27C2×#97C812yes—
28#349—24no—
29#349—42no—
30#341—44no—
31C23×C4—21no—
32C23×C4C22⋊C411yescharacteristic
33C2×M16—22no—
34C2×M16—22no—
35C2×M16—41no—
36C2×M16—42no—
37C2×M16—42no—
38C2×M16—42no—
39C2×M16—42no—
40C2×M16C22⋊C412yes—
41C2×M16C4⋊C412yes—
42C22×C8—22no—
43C22×C8—22no—
44C22×C8—22no—
45C22×C8—22no—
46C22×C8—41no—
47C22×C8—41no—
48C22×C8—41no—
49C22×C8—41no—
50C22×C8—41no—
51C2×C42—21no—
52C2×C42—21no—
53C2×C42—21no—
54C2×C42C4211yescharacteristic
55C2×C42C4⋊C411yescharacteristic
56C2×C42C2×C811yescharacteristic
57C2×C42C2×C811yescharacteristic
58C2×C42M1611yescharacteristic
59C2×C42M1611yescharacteristic
60M32—44no—
61M32—82no—
62C2×C16—82no—
63C4⋊C8—42no—
64C4⋊C8—41no—
65C4⋊C8—41no—
66C4⋊C8—42no—
67C4⋊C8—42no—
68#97—42no—
69#97—42no—
70C24#10111yescharacteristic
71C22×C4—21no—
72C22×C4—21no—
73C22×C4—21no—
74C22×C4—21no—
75C22×C4—21no—
76C22×C4—21no—
77C22×C4—21no—
78C22×C4—21no—
79C22×C4—21no—
80C22×C4—21no—
81C22×C4—82no—
82C22×C4#9511yescharacteristic
83C22×C4C22⋊C811yescharacteristic
84C22×C4C22⋊C811yescharacteristic
85C22×C4#9911yescharacteristic
86C22×C4#9911yescharacteristic
87C22×C4#10011yescharacteristic
88M16—42no—
89M16—42no—
90M16—44no—
91M16—82no—
92M16—82no—
93C2×C8—24no—
94C2×C8—22no—
95C2×C8—22no—
96C2×C8—42no—
97C2×C8—42no—
98C2×C8—42no—
99C2×C8—42no—
100C2×C8—42no—
101C2×C8—42no—
102C2×C8—42no—
103C2×C8—42no—
104C2×C8—42no—
105C2×C8—81no—
106C2×C8—81no—
107C42—21no—
108C42—21no—
109C42—21no—
110C42—21no—
111C42—21no—
112C42—21no—
113C42C4×C811yescharacteristic
114C42#9711yescharacteristic
115C42C4⋊C811yescharacteristic
116C42C4⋊C811yescharacteristic
117C16—84no—
118C23—21no—
119C23—21no—
120C23—42no—
121C23#32411yescharacteristic
122C23#32411yescharacteristic
123C23#34311yescharacteristic
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—21no—
127C2×C4—21no—
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—42no—
139C2×C4—42no—
140C2×C4—81no—
141C2×C4—81no—
142C2×C4—81no—
143C2×C4—81no—
144C2×C4#32311yescharacteristic
145C2×C4#32311yescharacteristic
146C2×C4#33611yescharacteristic
147C2×C4#34211yescharacteristic
148C2×C4#35311yescharacteristic
149C2×C4#35411yescharacteristic
150C2×C4#35511yescharacteristic
151C2×C4#35611yescharacteristic
152C8—44no—
153C8—42no—
154C8—42no—
155C8—82no—
156C22—22no—
157C22—21no—
158C22—21no—
159C22—41no—
160C22—41no—
161C22—42no—
162C22—42no—
163C22#128011yescharacteristic
164C22#132411yescharacteristic
165C22#132511yescharacteristic
166C4—21no—
167C4—21no—
168C4—41no—
169C4—41no—
170C4—41no—
171C4—41no—
172C4#131811yescharacteristic
173C4#131911yescharacteristic
174C4#139311yescharacteristic
175C4#139411yescharacteristic
176C2—21no—
177C2—21no—
178C2—41no—
179C2—41no—
180C2#718911yescharacteristic
181C2#737412yes—
subgroupG/H
centerC2×C4#353
commutatorC42C4×C8
Frattini, cosocleC2×#423C22
socleC22#1325
prime radicalC24#101
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C2×#423 ◁ G
LECSG ▷ C2×#423 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#13272
#108452